Question

Your friend claims that the measure of an exterior angle of a triangle can never be acute because it is the sum of the two nonadjacent angles of the triangle. Is your friend correct? Explain your reasoning

Answer 1

Answer: No, He is not correct.

Explanation:

Since we know that the sum of all interior angles of triangles is 180°.

And, If an exterior angle of a triangle is acute ⇒ The adjacent interior angle is obtuse

Also, we know that an exterior angle of a triangle is equal to the sum of the opposite interior angles

Therefore, the sum of two interior angles is acute.

'The total sum of the all interior angles of the triangle =One obtuse angle+ acute sum of the angles' can be equal to 180°.

For example let the exterior angle of a triangle is 80° ( acute)

Therefore, the adjacent angle of this exterior angle = 180-80=100°

And, sum of the opposite angles = 80°

Therefore total sum of the interior angles = 100 + 80 =180°

Thus, He was wrong.